| Evolutionary Algorithms such as Genetic Algorithms and Evolution Strategies are applied to the optimal design of groundwater in situ bioremediation. A finite element simulation model (BIO2D) is incorporated in the optimization to evaluate the aquifer response to design alternatives. For algorithm comparison, three bioremediation problems are examined: time-invariant 9-well (P-A: 9 decision variables), time-varying 9-well (P-B: 54 decision variables), and time-varying 6-well (P-C: 72 decision variables).; First, a Real-Coded Genetic Algorithm (RGA), which implements two operators (Directive Recombination and Screened Replacement) proposed in this study, is developed. RGA shows better performance than a standard Binary-Coded GA in efficiency and accuracy. Second, RGA and Derandomized Evolution Strategy (DES) are compared to direct search methods (Nelder-Mead Simplex (NSLX), Modified Simplex (MSLX), and Parallel Directive Search (PDS)) and derivative-based optimization methods (Implicit Filtering for Constrained Optimization (IFFCO) and Successive Approximation Linear Quadratic Regulator (SALQR)). For P-A, most of the algorithms produce good solutions, and MSLX shows the best performance. For P-B, both the direct search methods and IFFCO converge to local optima, and yield inaccurate solutions. SALQR most efficiently and accurately solves P-B, but it converges to local optima for P-C. Both RGA and DES produce more accurate solutions than the others for P-C, but RGA is less accurate and efficient than DES and SALQR for P-B. DES also provides a good solution to P-B with reasonable efficiency. Of the methods, DES appears particularly promising because it does not require derivative information and can be modified for efficient parallel processing. SALQR is particularly efficient for time-varying control problems which have many management periods. Third, a parallel algorithm called Parallel Derandomized Evolution Strategy (PADES) is developed by modifying DES. PADES shows very high speedups (92.7 for 100 processes) and efficiencies up to 100 processes. Fourth, because of the requirement of fixed-cost design in groundwater bioremediation, which is very difficult to solve with conventional optimization techniques, a Hybrid-Coded Evolutionary Algorithm (HCEA), which combines a Hybrid-Coded GA and PADES, is developed. Its results are compared with those of Penalty Coefficient method. Only HCEA identifies the optimal solutions to P-A and P-B. |
